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            <article class="content wrap" id="_content" data-uid="CADability.LinearAlgebra.SingularValueDecomposition">
  
  
  <h1 id="CADability_LinearAlgebra_SingularValueDecomposition" data-uid="CADability.LinearAlgebra.SingularValueDecomposition" class="text-break">Class SingularValueDecomposition
  </h1>
  <div class="markdown level0 summary"><p>Singular Value Decomposition.</p>
</div>
  <div class="markdown level0 conceptual"></div>
  <div class="inheritance">
    <h5>Inheritance</h5>
    <div class="level0"><span class="xref">System.Object</span></div>
    <div class="level1"><span class="xref">SingularValueDecomposition</span></div>
  </div>
  <div class="inheritedMembers">
    <h5>Inherited Members</h5>
    <div>
      <span class="xref">System.Object.Equals(System.Object)</span>
    </div>
    <div>
      <span class="xref">System.Object.Equals(System.Object, System.Object)</span>
    </div>
    <div>
      <span class="xref">System.Object.GetHashCode()</span>
    </div>
    <div>
      <span class="xref">System.Object.GetType()</span>
    </div>
    <div>
      <span class="xref">System.Object.MemberwiseClone()</span>
    </div>
    <div>
      <span class="xref">System.Object.ReferenceEquals(System.Object, System.Object)</span>
    </div>
    <div>
      <span class="xref">System.Object.ToString()</span>
    </div>
  </div>
  <h6><strong>Namespace</strong>: <a class="xref" href="CADability.LinearAlgebra.html">CADability.LinearAlgebra</a></h6>
  <h6><strong>Assembly</strong>: CADability.dll</h6>
  <h5 id="CADability_LinearAlgebra_SingularValueDecomposition_syntax">Syntax</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">[Serializable]
public class SingularValueDecomposition</code></pre>
  </div>
  <h5 id="CADability_LinearAlgebra_SingularValueDecomposition_remarks"><strong>Remarks</strong></h5>
  <div class="markdown level0 remarks"><p>For an m-by-n matrix A with m >= n, the singular value decomposition 
is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
an n-by-n orthogonal matrix V so that A = U*S*V&apos;.</p>
<p>The singular values, sigma[k] = S[k, k], are ordered so that
sigma[0] >= sigma[1] >= ... >= sigma[n-1].</p>
<p>The singular value decompostion always exists, so the constructor will
never fail.  The matrix condition number and the effective numerical
rank can be computed from this decomposition.</p>
</div>
  <h3 id="constructors">Constructors
  </h3>
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  <a id="CADability_LinearAlgebra_SingularValueDecomposition__ctor_" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.#ctor*"></a>
  <h4 id="CADability_LinearAlgebra_SingularValueDecomposition__ctor_CADability_LinearAlgebra_Matrix_" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.#ctor(CADability.LinearAlgebra.Matrix)">SingularValueDecomposition(Matrix)</h4>
  <div class="markdown level1 summary"><p>Construct the singular value decomposition.</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public SingularValueDecomposition(Matrix Arg)</code></pre>
  </div>
  <h5 class="parameters">Parameters</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Name</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><a class="xref" href="CADability.LinearAlgebra.Matrix.html">Matrix</a></td>
        <td><span class="parametername">Arg</span></td>
        <td><p>Rectangular matrix</p>
</td>
      </tr>
    </tbody>
  </table>
  <h5 id="CADability_LinearAlgebra_SingularValueDecomposition__ctor_CADability_LinearAlgebra_Matrix__remarks">Remarks</h5>
  <div class="markdown level1 remarks"><p>Provides access to U, S and V.</p>
</div>
  <h3 id="properties">Properties
  </h3>
  <span class="small pull-right mobile-hide">
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    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_SingularValueDecomposition_LeftSingularVectors.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.SingularValueDecomposition.LeftSingularVectors%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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  <a id="CADability_LinearAlgebra_SingularValueDecomposition_LeftSingularVectors_" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.LeftSingularVectors*"></a>
  <h4 id="CADability_LinearAlgebra_SingularValueDecomposition_LeftSingularVectors" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.LeftSingularVectors">LeftSingularVectors</h4>
  <div class="markdown level1 summary"><p>Gets the left singular vectors (U matrix).</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public Matrix LeftSingularVectors { get; }</code></pre>
  </div>
  <h5 class="propertyValue">Property Value</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><a class="xref" href="CADability.LinearAlgebra.Matrix.html">Matrix</a></td>
        <td></td>
      </tr>
    </tbody>
  </table>
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  <a id="CADability_LinearAlgebra_SingularValueDecomposition_RightSingularVectors_" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.RightSingularVectors*"></a>
  <h4 id="CADability_LinearAlgebra_SingularValueDecomposition_RightSingularVectors" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.RightSingularVectors">RightSingularVectors</h4>
  <div class="markdown level1 summary"><p>Gets the right singular vectors (V matrix).</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public Matrix RightSingularVectors { get; }</code></pre>
  </div>
  <h5 class="propertyValue">Property Value</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><a class="xref" href="CADability.LinearAlgebra.Matrix.html">Matrix</a></td>
        <td></td>
      </tr>
    </tbody>
  </table>
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    <span class="divider">|</span>
    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_SingularValueDecomposition_S.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.SingularValueDecomposition.S%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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  <a id="CADability_LinearAlgebra_SingularValueDecomposition_S_" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.S*"></a>
  <h4 id="CADability_LinearAlgebra_SingularValueDecomposition_S" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.S">S</h4>
  <div class="markdown level1 summary"><p>Get the diagonal matrix of singular values.</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public Matrix S { get; }</code></pre>
  </div>
  <h5 class="propertyValue">Property Value</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><a class="xref" href="CADability.LinearAlgebra.Matrix.html">Matrix</a></td>
        <td></td>
      </tr>
    </tbody>
  </table>
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    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_SingularValueDecomposition_SingularValues.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.SingularValueDecomposition.SingularValues%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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  <a id="CADability_LinearAlgebra_SingularValueDecomposition_SingularValues_" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.SingularValues*"></a>
  <h4 id="CADability_LinearAlgebra_SingularValueDecomposition_SingularValues" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.SingularValues">SingularValues</h4>
  <div class="markdown level1 summary"><p>Gets the one-dimensional array of singular values.</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public double[] SingularValues { get; }</code></pre>
  </div>
  <h5 class="propertyValue">Property Value</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><span class="xref">System.Double</span>[]</td>
        <td><p>diagonal of S.</p>
</td>
      </tr>
    </tbody>
  </table>
  <h3 id="methods">Methods
  </h3>
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  <a id="CADability_LinearAlgebra_SingularValueDecomposition_Condition_" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.Condition*"></a>
  <h4 id="CADability_LinearAlgebra_SingularValueDecomposition_Condition" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.Condition">Condition()</h4>
  <div class="markdown level1 summary"><p>Two norm condition number.</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public double Condition()</code></pre>
  </div>
  <h5 class="returns">Returns</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><span class="xref">System.Double</span></td>
        <td><p>max(S)/min(S)</p>
</td>
      </tr>
    </tbody>
  </table>
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    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_SingularValueDecomposition_Norm2.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.SingularValueDecomposition.Norm2%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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  <a id="CADability_LinearAlgebra_SingularValueDecomposition_Norm2_" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.Norm2*"></a>
  <h4 id="CADability_LinearAlgebra_SingularValueDecomposition_Norm2" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.Norm2">Norm2()</h4>
  <div class="markdown level1 summary"><p>Two norm.</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public double Norm2()</code></pre>
  </div>
  <h5 class="returns">Returns</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><span class="xref">System.Double</span></td>
        <td><p>max(S)</p>
</td>
      </tr>
    </tbody>
  </table>
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  <h4 id="CADability_LinearAlgebra_SingularValueDecomposition_Rank" data-uid="CADability.LinearAlgebra.SingularValueDecomposition.Rank">Rank()</h4>
  <div class="markdown level1 summary"><p>Effective numerical matrix rank.</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public int Rank()</code></pre>
  </div>
  <h5 class="returns">Returns</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><span class="xref">System.Int32</span></td>
        <td><p>Number of nonnegligible singular values.</p>
</td>
      </tr>
    </tbody>
  </table>
</article>
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